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2017 East Central NA Regional Contest

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2017-10-28 19:00 UTC

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Problem DGame of Throwns

Daenerys frequently invents games to help teach her second
grade Computer Science class about various aspects of the
discipline. For this week’s lesson she has the children form a
circle and (carefully) throw around a petrified dragon egg.

The $n$ children are
numbered from $0$ to
$n - 1$ (it is a Computer
Science class after all) clockwise around the circle. Child
$0$ always starts with the
egg. Daenerys will call out one of two things:

a number $t$,
indicating that the egg is to be thrown to the child who is
$t$ positions
clockwise from the current egg holder, wrapping around if
necessary. If $t$ is
negative, then the throw is to the counter-clockwise
direction.

the phrase undo $m$, indicating that the last
$m$ throws should be
undone. Note that undo commands never
undo other undo commands; they just
undo commands described in item $1$ above.

For example, if there are $5$ children, and the teacher calls
out the four throw commands 8 -2 3 undo 2,
the throws will start from child $0$ to child $3$, then from child $3$ to child $1$, then from child $1$ to child $4$. After this, the undo 2 instructions will result in the egg being
thrown back from child $4$
to child $1$ and then from
child $1$ back to child
$3$. If Daenerys calls out
$0$ (or $n, -n, 2n, -2n$, etc.) then the child
with the egg simply throws it straight up in the air and
(carefully) catches it again.

Daenerys would like a little program that determines where
the egg should end up if her commands are executed correctly.
Don’t ask what happens to the children if this isn’t the
case.

Input

Input consists of two lines. The first line contains two
positive integers $n$$k$ ($1\leq n \leq 30$, $1 \leq k \leq 100$) indicating the
number of students and how many throw commands Daenerys calls
out, respectively. The following line contains the $k$ throw commands. Each command is
either an integer $p$
($-10\, 000 \leq p \leq 10\,
000$) indicating how many positions to throw the egg
clockwise or undo$m$ ($m
\geq 1$) indicating that the last $m$ throws should be undone. Daenerys
never has the kids undo beyond the start of the game.